Factor analysis is often used to explore the structure of tests and questionnaires used in the biological, behavioral, and social sciences, In certain situations the researcher is interested in comparing the factor solutions of two tests. Since factor matrices are only defined up to an orthogonal rotation it is not ususally appropriate to directly compared the two solutions. By defining two orthogonal factor solutions to be equivalent if one can be orthogonally rotated to perfectly fit the other, psychometricians have developed procedures and goodness of fit measures for comparing two orthogonal factor solutions. They label this problem "the Orthogonal Procrustes Problem." However, the psychometricians do not develop any stochastic properties of their measures and thus no procedure is available for testing the hypothesis that two tests have the same factor solution. The preliminary results given in the appendix develop such a hypothesis test. The purpose of this project will be to expand these preliminary results by studying the stochastic properties of the goodness of fit measures, writing a computer program which will test the hypothesis of equivalent factor solutions, applying these measures to non-metric scaling solutions, and finally extending the entire approach to the problem of comparing oblique factor solutions.